Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane
Analysis of PDEs
2015-05-05 v1
Abstract
This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these equations defined in the upper half-plane. Under suitable growth conditions on the flux function, we are able to establish the global well-posedness in a Sobolev class. When the initial- and boundary-data become more regular, the corresponding solutions are shown to be classical. In addition, the continuous dependence on the data is also obtained.
Keywords
Cite
@article{arxiv.1505.00425,
title = {Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane},
author = {Ying-Chieh Lin and C. H. Arthur Cheng and John M. Hong and Jiahong Wu and Juan-Ming Yuan},
journal= {arXiv preprint arXiv:1505.00425},
year = {2015}
}